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Proof step 13 from proof sum-countFun-sub (previous step)

0 ≤ i, j < i, ∀ j0, i, intfun, intfun0. i→n(j0) < i→n(j) → 0 ≤ i → Σ countFun(i, j0, intfun) = Σ countFun(i, j0, λ i0. intfun(i0) - intfun0(i0)) + Σ countFun(i, j0, intfun0) ⊦ 0 = Σ countFun(i, j, λ i0. intfun(i0) - intfun0(i0))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: countFun-base seq: ⊦ j < i → countFun(i, j, intfun) = [] subst: [intfun, j, i] → [λ i0. intfun(i0) - intfun0(i0), j, i] flags: rewrite, current

Additional information

Used simplifier rules: sum-empty: ⊦ Σ [] = 0; Used terms: λ i0. intfun(i0) - intfun0(i0), j, i